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The matrix H can be different expressions corresponding to what is called zeroth-order, first-order, and higher-order regularization. Each of these corresponds to difference approximations of derivatives of various orders. The zeroth order regularization is the most common, and its H is simply the identity matrix I; the effect of zeroth-order regularization is to bias the parameter estimates toward zero. The first-order regularization corresponds to the first derivative with time, if the desired function is a function of time.
K. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green’s Functions, Hemisphere, Washington, DC, 1992. 26. Tikhonov, A. , The Stability of Inverse Problems, Doklady Akad. Nauk SSSR, Vol. 39, 1943. 27. Tikhonov, A. , Regularization of Ill-posed Problems, Doklady Akad. Nauk SSSR, Vol. 153, 1963. book Page 41 Monday, August 12, 2002 6:43 PM chapter two Sequential function specification method using future times for function estimation Keith A. Woodbury Contents Abstract Nomenclature Superscripts Subscripts Greek symbols Introduction Direct vs.
Iter. 15). 0001, the residuals (indicated by the circles) are mainly affected by the modeling error. We have a characteristic signature that would be repeated again and again for other sets of random errors with the same σ. Note that the maximum amplitude occurs at the final time and is negative. That would be expected from the heat loss. 4, which is for a related case and has the same characteristic. 1 model. Heat losses are not modeled. 01. signature is virtually invisible. 01) were run and the residuals averaged.